Part a
For this case we have two points given (1,3) and (4,6) and we want to find the equation for this line and we can use this equation:
[tex]y=mx+b[/tex]Where m represent the slope and b the intercept. We can estimate the slope with this formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{6-3}{4-1}=1[/tex]And then we can find the intercept from one point given and replacing into the equation like this:
[tex]3=1\cdot1+b\rightarrow b=2[/tex]And the equation would be:
[tex]y=x+2[/tex]Part b
Now we just need to see if the point (1,3) is on the line calculated let's check this. If x=1 we have that:
[tex]y=1\cdot1+2=3[/tex]So then we verify that the point is on the line and then that would be the proof for this case.
